fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) & p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) | p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,![X0_2E0]: (~ (p(s(tyop_2Emin_2Ebool,X0_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,![X0_2E0, X1_2E0]: ((p(s(tyop_2Emin_2Ebool,X0_2E0)) => p(s(tyop_2Emin_2Ebool,X1_2E0))) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))))).
fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0, X1_2E0]: ((s(A_27a,X0_2E0) = s(A_27a,X1_2E0)) <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))))).
fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,![A_27a]: ![X0_2E0]: (s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))))).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27state_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,![A_27a, A_27b, A_27state]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0))))).
fof(arityeq1_2Ec_2Estate__transformer_2EWIDEN_2E1_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27state,axiom,![A_27a, A_27b, A_27state]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Estate__transformer_2EWIDEN_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Estate__transformer_2EWIDEN_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),X0_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27state_29,axiom,![A_27a, A_27b, A_27state]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27state),X1_2E0))))).
fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2EA_27state,axiom,![A_27b, A_27state]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(A_27state,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(A_27state,X1_2E0))))).
fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27state_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,![A_27a, A_27b, A_27state]: ![X0_2E0, X1_2E0]: (s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27state),X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),X0_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27state),X1_2E0))))).
fof(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27state_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27b_2CA_27state_29_29,axiom,![A_27a, A_27b, A_27state]: ![X0_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),X0_2E0))))).
fof(state__transformerTheory_2EWIDEN__def,axiom,![A_27a, A_27b, A_27state]: ![F1_2E0, F0_2E0]: (![V1s1_2E0, V3r_2E0, V4s3_2E0]: (s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F1_2E0),s(A_27b,V1s1_2E0))),s(A_27a,V3r_2E0))),s(A_27state,V4s3_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Epair_2E_2C_2E2(s(A_27a,V3r_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27state),c_2Epair_2E_2C_2E2(s(A_27b,V1s1_2E0),s(A_27state,V4s3_2E0)))))) => (![V0f_2E0, V1s1_2E0, V2s2_2E0]: (s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0))),s(A_27b,V1s1_2E0))),s(A_27state,V2s2_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F1_2E0),s(A_27b,V1s1_2E0))))),s(tyop_2Epair_2Eprod(A_27a,A_27state),app_2E2(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0),s(A_27state,V2s2_2E0)))))) => ![V0f_2E0]: (s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Estate__transformer_2EWIDEN_2E1(s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27state),tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,tyop_2Epair_2Eprod(A_27b,A_27state))))),F0_2E0),s(tyop_2Emin_2Efun(A_27state,tyop_2Epair_2Eprod(A_27a,A_27state)),V0f_2E0))))))))).
